This is another one of those postings that I make almost entirely for my own benefit. Today at lunch I was having a discussion with Tom about a particular problem that I was having trouble understanding: namely, understanding why the formulas for optimal sizing of pinhole camera aperatures were, well, what they are. Where do the numbers come from and why? It turns out that you can express the problem in terms of integrals of complex exponentials defined over the aperature, which seems obvious in most respects, but left me with the desire to actually compute some analytic integrals, and let’s face it, it’s been two decades since I did anything more complicated than ordinary polynomials. Tom mentioned the Risch algorithm which I had never heard of before, and while my brain seems too tired to absorb it at the moment, it seems like the kind of thing I’ll look into later, so this is just a reminder.

[tags]Mathematics,Symbolic Integration[/tags]

Addendum: the image generated by a point light source by a finite aperature at a given wavelength assumes the form of an Airy disk. I wrote the equations out in gnuplot to make the following graph.